Use biggest soldering iron available.
Firstly add some more new solder to each lead so you have a good fresh contact patch that will easily transfer heat into joint.
To desolder, it is good if you can heat both leads with the iron tip at once - if not move iron to & fro between pins every few seconds so they both melt at about the same time.
Adding a little more solder as you heat may help - heat lead with iron and feed solder wire into space against iron and tip so liquid solder flows over joint and helps transfer heat.
Once BOTH leads are well melted pull on cap away from board and simultaneously do as user 6792 says and tap board on a surface or edge to persuade solder to all leave at once.
If above dopes not work you can try melting both joints and then pushing cap sideways along line between leads so one lead pulls clear as you have formed a level with short distance between leads being one leg and height of cap (and your arm and muscle system) being parts of the other. Once one lead pulls clear or partly so, repeat with force such as to pull out other lead.
Note that this puts stress on cap internals and may cause damage, as will prolonged heat.
Having a desoldering tool / solder pump / solder sucker ... is useful.
"Solder wick" can work very well.
Not as good on multi layer boards.
Add new solder,
place wick on solder,
heat solder through wick,
move new wick into place as required until clean.
Using solder wick - 1:42 you tube
Similar - I find that heating THROUGH the braid as at about 3 minutes in video is most effectice.
Text and diagrams
Looks like this
Make sure voltage ratings suit new use.
Big caps that have had extensive use will have reduced lifetimes - still can be very useful but they do "wear out".